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MODELS FOR FROZEN-FREE-SPLIT PHENOMENA IN e- -IRRADIATED Al AND Al-Fe
K.-H. Robrock, H. Schober
To cite this version:
K.-H. Robrock, H. Schober. MODELS FOR FROZEN-FREE-SPLIT PHENOMENA IN e- - IRRADIATED Al AND Al-Fe. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-735-C5-740.
�10.1051/jphyscol:19815113�. �jpa-00220982�
JOURNAL DE PHYSIQUE
CoZZoque C5, suppZEment au nO1O, Tome 42, octobre 1981 page C5-735
MODELS FOR FROZEN-FREE-SPLIT PHENOMENA IN
e--IRRADIATED A1 AND A1-Fe -
K.-H. Robrock and H . R . Schober
I n s t i t u t fiir E'estkiirperforschmg, KemforschungsanZage JuZich, 0-5170 JuZich, F. R. G.
A b s t r a c t . - Samples of pure Al and Al c o n t a i n i n g 400 atppm Fe have been i r r a - d i a t e d with e l e c t r o n s a t 4.2K and annealed a t subsequently h i g h e r tempera- t u r e s . During t h e a n n e a l i n g program i n pure Al, t h e growth and decay of two p a i r s of mechanical r e l a x a t i o n peaks was observed, and i n &-Fe of one p a i r . The members of' each p a i r grow and decay i n a p a r a l l e l f a s h i o n . They a r e ex- p l a i n e d a s b e i n g due t o t h e s t r e s s induced occupation of two d i f f e r e n t s e t s of e l a s t i c energy l e v e l s v i a two d i f f e r e n t r e l a x a t i o n modes by t h e r e o r i e n t a - t i o n of t h e
same
d e f e c t . For t h e p a i r s i n pure A1 and f o r t h e p z i r observed i n &-Fe a t o m i s t i c models a r e given based on computer s i m u l a t i o n s t u d i e s .I n t r o d u c t i o n . - Many examples a r e known where i r r a d i a t i o n induced s e l f - i n t e r s t i t i a l atoms give r i s e t o mechanical r e l a x a t i o n peaks /1,2/. I n t h e c a s e of pure
Al,
t h e s e peaks were a t t r i b u t e d t o s i n g l e and m u l t i p l e s e l f - i n t e r s t i t i a l s ( S ) / 3 , 4 / , and i n A1-Fe t o s o - c a l l e d SI-complexes, which c o n s i s t of one o r s e v e r a l s e l f - i n t e r s t i t i a l s-
bound a t an impurity atom (I) /5/. Since t h e peak h e i g h t s a r e p r o p o r t i o n a l t o t h e c o n c e n t r a t i o n s of t h e d e f e c t s r e s p o n s i b l e f o r t h e p e a k s , it i s p o s s i b l e t o f o l l o w t h e change of c o n c e n t r a t i o n s of i n d i v i d u a l d e f e c t s d u r i n g t h e course of an isochro- n a l tempering t r e a t m e n t . In some c a s e s it was observed, t h a t two peaks of t h e r e - l a x a t i o n spectrum showed t h e same a n n e a l i n g behaviour i n c o n t r a s t t o t h e d i f f e r e n t behaviour of t h e o t h e r s . This p a r a l l e l a n n e a l i n g must be c o n s i d e r e d a s a v e r y s t r o n g i n d i c a t i o n , t h a t each peak d o u b l e t i s caused by one d e f e c t v i a two s e p a r a t e r e l a x a - t i o n modes r a t h e r t h a n by two d i f f e r e n t d e f e c t s . This phenomenon h a s been named
"frozen-free-splitt'-phenomenon i n t h e l i t e r a t u r e / 6 / . The aim o f t h e p r e s e n t a r t i c l e i s t o d e s c r i b e a t o m i s t i c models, by wnich t h e occurance of double r e l a x a - t i o n modes observed i n pure A 1 and &-Fe can b e e x p l a i n e d .
Experimental.- D e t a i l s of t h e experiments a r e d e s c r i b e d elsewhere / 3 , 4 , 5 / . The i r r a - d i a t i o n s were performed a t t h e low temperature i r r a d i a t i o n f a c i l i t y of KFA J i i l i c h a t 4.2K w i t h 3 MeV e l e c t r o n s . The e l a s t i c a f t e r e f f e c t measurements on A 1 were c a r r i e d o u t i n a t o r s i o n a l pendulum u s i n g a l a s e r i n t e r f e r o m e t e r t e c h n i q u e , t h e i n t e r n a l f r i c t i o n measurements on A1 and g - F e i n t h e same a p p a r a t u s , u s i n g an e l e c t r o m a g n e t i c p i c k up system. The c o n c e n t r a t i o n o f r a d i a t i o n induced d e f e c t s were monitored by simultaneously i r r a d i a t e d r e s i s t i v i t y samples.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815113
C5-736 JOURNAL DE PHYSIQUE
R e s u l t s . - In T i g . 1 and 2 , t h e r e s u l t s a r e shown. m e r e s p e c t i v e u p p e r f i g u r e s d i s - p l a y t h e r e l a x a t i o n s p e c t r a of e l e c t r o n i r r a d i a t e d A 1 and Q-Fe, f o r a f i x e d r e l a x a - t i o n t i m e . The b a r s i n d i c a t i n g t h e peaks a r e p o s i t i o n e d a t t'nose t e m p e r a t u r e s , where t h e p r o c e s s e s h a v e a r e l a x a t i o n t i m e o f 100s ( A l ) and 0 . 0 4 s ( 4 - F e ) , r e s p e c t i v e l y . The h e i g h t s of t h e b a r s c o r r e s p o n d t o t h e maximum peak h e i g h t s , A o , o b t a i n e d d u r i n g t h e t e m p e r i n g t r e a t m e n t .
I
Temperature T I K I "l - - - - -
-
Peok 11 1 ? a
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I
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EOLL2 .
.
. . c. .
, ,- 0
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o
1
Peak 2
1
0 100 200 300
Anneollng Temperature To I K 1
F i g . 1 F i g . 2
' f i e r e s p e c t i v e ,Jpper f i g u r e s r e p r e s e n t a s c h e m a t i c view o f t h e m e c h a n i c a l r e l a x a - t i o n s p e c t r u m o f e l e c t r o n i r r a d i a t e d N a t T = 100s and g - F e a t T = 0 . 0 4 s , where
T i s t h e relaxation t i m e . The r e l a x a t i o n s t r e n e t h , A o , i s t h e l a r g e s t v a l u e ob- t a i n e d d u r i n g an 10 min i s o c h r o n a l a n n e a l i n g t r e a t m e n t . The r e s p e c t i v e l o w e r c u r v e s show t h e b u i l d - u p and r e c o v e r y o f t h e d i f f e r e n t r e l - a x a t i o n p e a k s o b s e r v e d d u r i n g t h e a n n e a l i n g t r e a t m e n t .
Below t h e n o r m a l i z e d peak h e i g h t s ,
A I L o ,
a r e p l o t t e d a s a f u n c t i o n o f a n n e a l i n g t e m p e r a t u r e . I n p u r e A l , p r o c e s s M h a s been i d e n t i f i e d a s t h e m i g r a t i o n and simul-1
t a n e o u s r e o r i e n t a t i o n p r o c e s s o f t h e s i n g l e s e l f - i n t e r s t i t i a l i n form o f 100-dumb- b e l l s / 3 / . As t h e s e m i g r a t e , t h e y may e n c o u n t e r o t h e r s e l f - i n t e r s t i t i a l s o r t h e Fe-atoms i n s o l u t i o n , w i t h which t h e y form e i t h e r multip1.e s e l f - i n t e r s t i t i d s i n t h e c a s e o f p u r e A l , o r SI-complexes i n t h e c a s e o f &-Fe. The f a c t t h a t p r o c e s s e s R o , R 2 and p a r t i a l l y R,, i n A 1 as w e l l a s p r o c e s s e s 1 and 4 i n &-Fe grow p a r a l l e l w i t h t h e d e c a y of M I h a s l e d t o t h e c o n c l u s i o n , t h a t t h e s e p r o c e s s e s a r e c a u s e d by r e a c t i o n p r o d l ~ c t s o f t h e m i g r a t i n g s e l f - i n t e r s t i t i a l s : M u l t i p l e s e l f - i n t e r s t i - t i a l s i n t h e c a s e o f p u r e A 1 and SI-complexes i n t h e c a s e o f &-Fe. The r e m a r k a b l e f e a t u r e i s n o t o n l y t h a t a l l t h e s e p r o c e s s e s a p p e a r i n a p a r a ] - l e l f a s h i o n , b u t t h a t t h e y f o l l o w p a i r w i s e t h e same beha.viour d u r i n g t h e s u b s e q u e n t t e m p e r i n g treatment;:
The ( R 2 , M ~ ) - d o u b l e t d e c a y s i n a narrow t e m p e r a t u r e r a n g e around
4 7 ~ ,
t h e (n0,Rh)- d o u b l e t r e m a i n s c o n s t a n t up t o a b o u t 6 0 ~ and a l s o d e c a y s i n a narrow t e m p e r a t u r e r a n g e t o z e r o . F i n a l l y , t h e ( l , 4 ) - d o u b l e t i n g - F e d e c a y s i n a p a r a l l e l f a s h i o n b y a b o u t 1 5 % between 80K and 200K, and t h e n i n a s t e p t o z e r o a t 220K.The a n n e a l i n g c u r v e s of t h e o t h e r p r o c e s s e s R 1 , R3, R and 3 , 3, 5 ,
6
f o l l o w 5e n t i r e l y d i f f e r e n t t r e n d s t h a n t h o s e o f t h e p a i r c d p e a k s .
U i s c u s s i o n . - l'he p a r a l l e l b e h a v i o u r o f t h e two members o f e a c h of t h e p a i r s i s a r a t h e r s t r o n g i n d i c a t i o n , t h a t t h e y r e s u l t from t h e r e o r i e n t a t i o n o f t h e
same
de- f e c t v i a two d i f f e r e n t r e l a x a t i o n modes r a t h e r t h a n from two d i f f e r e n t d e f e c t s , which undergo f o r t u i t o u s l y t h e same r e a c t i o n s d u r i n g t h e t e m p e r i n e t r e a t m e n t . T h i s view is s u p p o r t e d by r e c e n t computer s i m u l a t i o n s t u d i e s /'(-lo/ of t h e s t a b i l i t y and m o b i l i t y of d i f f e r e n t s e l f - i n t e r s t i t i a l - c o n f i g u r a t i o n s which w i l l b e d i s c u s s e d i n t h e f o l l o w i n g .One o f t h e o u t s t a n d i n g p r o p e r t i e s o f t h e
<loo>
dumbbell s e l f - i n t e r s t i t i a l i s i t s c a p a b i i i t y t o perform low f r e q u e n c y r e s o n a n t l i b r a t i o n modes. These have b e e n found f o r s i n g l e<loo>
d u m b b e l l s / 8 / , f o r dumbbells which a r e members i n a m u l t i p l e i n t e r - s t i t i a l/7/
and a l s o i.or mixed dumbbells/ a / .
These l i b r a t i o n modes are v e r y s e n s i - t i v e t o p e r t u r b a t i o n s , and c a n b e made l o c a l l y u n s t a b l y b y s m a l l e s t changes i n t h e p o t e n t i a l u s e d i n t h e computer s i m u l a t i o n . These l o c a l i n s t a b i l i t i e s may c a u s e a tilt o f t h e dumbbell away from t h e e x a c t <001> d i r e c t i o n f o r up t o 10'. Such t i l t s have b e e n found f o r d i i n t e r s t i t i a l s / 7 / and f o r mixed dumbbells / 9 / .The d i i n t e r s t i t i a l c o n s i s t i n g o f two p a r a l l e l t i l t e d d u m b b e l l s i s shown i n f i g . 3. F i g . 3a shows t h e two e q u i v a l e n t o r i e n t a t i o n s , which t h e s e dumbbells may occupy. T r a n s i t i o n s between t h e s e two may c a u s e a n I F peak w i t h an a c t i v a t i o n
F i g . 3: ( a ) " T i l t w - j u m p and ( b ) 90'-jumps o f t h e d i i n t e r s t i t i a l atom c o n s i s t i n g o f two p a r a l l e l t i l t e d d u m b b e l l s .
C5-738 JOURNAL DE PHYSIQUE
e n e r g y o f t h e o r d e r of 0.01 eV a c c o r d i n g t o t h e computer simul.a%ion. T h i s d i i n t e r - s t i t i a l may undergo a second r c o r i e n t a t i o n a s shown i n f i g . 3 b , which i s e x p e c t e d t o g i v e r i s e t o a second r e l a x a t i o n e f f e c t w i t h an a c t i v a t i o n e n e r g y o f t h e o r d e r o f 0 . 1 eV. T h i s l a t t e r j u m p c a ~ ; s e s s i m u l t a n e o u s l y w i t h t h e r e o r i e n t a t i o n e f f e c t a l o n g r a n g e d i f f u s i o n o f t h c d i i n t e r s t i t i a l . T h i s i s e x a c t l y whet h a s b e e n o b s e r v c d f o r t h e peak p a i r (R M ) where ir! R2 o n l y a l o c a l reorientation i s i n v o l v e d ,
2 ' 2
'
whereas i n M2 i n a d d i t i o n t o $he r e o r i e n t a t i o n a l o n g r a n g c d i f f u s i o n o c c u r s / 4 / . The o n l y s e r i o u s d i s c r e p a n - y i n t h i s r r s s i p m c n t l i e s i n t h e f a c t , t h a t t h e e x p e r i - m e n t a l l y o b s e r v c d a c t i v a t i o n e n e r a o f R 2 , which i s 0 . 0 9 eV i s nuch h i g h e r t h a n ex- p e c t e d f o r a s l i g h t l y t i i t e d dumbbell.
L a r g e r m u l t i p l e i n t e r s t i t i a l a t o n s may a l s o c o n t e i n t i l t e d d u m b b e l l s . T i l t - j u m p s and 9 0 ~ - j w n ~ s a s b e f o r e o f dumbbells i n one o l t h e s e n u l t i p 1 . e interstitial atoms nay b e invoked t o a c c o u n t f o r t h e o c c u r c n c e of t h c second peak d o u b l e t ( R R ) ob-
0 ' 4 s e r v e d i n A l .
The <001>-mixeci d u n b b e l l i s shown i n f i g . 4 a , where an i m p u r i t y atom and a h o s t atom a r e members of he dumbbell. Tilere a r e 6 e q u i v a l e n t p o s i t i o n s o f t h e mixed d+
b e l l a r o u n d t h e o c t ~ h e d r a l c e n t r e , where t h e impuri.ty-end p o i n t s always t o t h i s cen- t r e . R e o r i e n t a t i o n jumps may o c c u r by j:unps of t h e impurity-atom from one s i t e t o a n o t h e r l i k e i n a c a g e .
F i g . 4 a : The <001> x i x e d d u n b b e l l w i t h t h e "cageff i n which t h e i m p u r i t y may r a t t l e a r o u n d .
F i e . 4b: T i l t e d mixed dumbbell. The f o u r f o l d dcgerleracy o f t h e c o r n e r s o f t h e o c t a - h e d r a l cage i s l i f c e d . Two ,jumps a t d i f f e r e n t r a t e s v , and v 2 o c c u r u i t h - i n t h e s q u a r e s and f'rom ope s q u a r e t o t h c o t h e r , r e s p e c t i v e l y .
F i g . 4 c : S p l i t L r i g o n a l c a g e . I t d e v e l o p s from t h e p r e v i o u s one (Pip;. 4 b ) by i n - c r e a s i n g t h e s i z e of t h e s q u a r e s , whereby t h e s i z e o f t h e t r i a n g l e s de- c r e a s e s .
If t h e dumbbell i s t i l t e d t h e ' o u r f o l d d e g e n e r a c y of t h e c o r n e r s o f t h e o c t a h e -
& a 1 c a g e i s l i f t e d and a new c a g e w i t h 24 e q u i v a l e n t c o n f i g u r a t i o n s i s formed a s shown i n f i g . hb. Two d i f f e r e n t jumps c a n occw i n t h i s c a g e : j u a p s w i t h i n e a c h o f
t h c s q u a r e s a t a r a t e v l , and jumps from one s q u a r e t o a n o t h e r a t a r a t e v 2 ' Although t h i s " t i l t e d " d m b b e l l model e x p l a i n s i n p r i n c i p l e t h e o c c u r e n c e o f a peak d o u b l e t b e c a u s e of t h e two d i f f e r e n t jumps, i t t u r n s o u t t h a t t h e peak p a i r
( 1 , 4 ) i n A1-Fe cannot b e e x p l a i n e d by t h i s model S e c a u s e of t h c f o l l o w i n g p e c u 1 j . w p r o p e r t y o f t h i s p a i r : Both p e a k s a r e c k l a r a c t e r i z c d by & C # 0 and 6C'
2
0 , i . e . b o t h p e a k s a r e i n d u e d by a p u r e C-shear d e f o r m a t i o r ~ / 5 / . I n o r d e r t o a c c o u n t f o r t h e non v a n i s h i n g r e l a x a t i o n s t r e n g t h o f t h e h i g h t e m p e r a t u r e peak ( 4 ) i t i s ne- c e s s a r y t o assume t h a t t h e f u l l thermodynamic e q u i l i b r i u m d i s 1 ; r i b u t i o n o f t h e Fe- atoms among t h e 2 4 r o s i t i o n s c a n o n l y b e a c h i e v e d by t h e u2-junps, and a l r e a d y n o t by t h e v jumps a t low t e m p e r a t u r e s . I t t u r n s o u t now t h a t t h i s requirement i s jusl,1
n o t f ' u l f i l l c d by t h e t i l t e d dumbbell: The s y s t e m can a l r e a d y r c l a x i n t o t h e f i n a l . e q u i l i b r i u m v i a vl-jumps s o l e l y / 9 / , and t h e r e f o r e a second peak under a C-defor- ma ti or^ c a n n o t b c e x p l a i n e d d e s p i t e o f t h c two d i f f ' e r e n t jump modes.
S e v e r a l o t h e r cage s t r u c t u r e s have been examined. One p o s s i b l e c a n d i d a t e , which would e x p l a i n t h e p r e s e n t observations i s shown i n f i g . 4 c . T h i s cage cen b e en- v i s a g e d a s devel.oping from t h e p r e v i o u s one by i n c r e a s i n g t h e s q u a r e s , whereby t h c s i z e of t r i a n g l e s d e c r e a s c s . A s !.he s e p a r a t i o n i n t h e t r i a n g l e becomes smal.1, t h e low t e m p e r a t u r e peak wou1.d o c c u r v i a jumps i n t h e t r i a n g l . e , and t h e h i g h tempera- t u r e peak v i a jumps i n t h e s q u a r c s . T h i s cage c o u l d i n f a c t a c c o u n t for a l l t h e p r o p e r t i e s o f t h e peak d o u b l e t ( 1 , 4 ) i n A1-Fe.
There i s however a s e v e r e o b j e c t i o n e g a i n s t t h i . s model coming from a n e n t i r e l y d i f f e r e n t s i d e : T h e l o c e l i z c d d i f f u s i o n o f t h e F'e-atoms i n a cage h a s a l s o been ob- s e r v e d r e c e n t l y by Mijljbauer measuremcrits / I ? / . The r e s u l t s of t h e s e measurements however a r e n o t i n egreement w i t h t h e cage shown i n f i g . k c , i..e
.
t h e cage which e x p l a i n s t h e IF-peaks w e l l d o e s n o t s o f o r t h e MoDbauer measurements / 1 2 / . A l l c a g e s c o m p a t i b l e w i t h t h e c u b i c symmetry o f t h e f c c l s t t . i c e c o n t a i n i n g up t o 31+ i n - t e r s t i t i a l s i t e s f o r t h e s o l u t e atom have b e e n examined. There a r e two o t h e r c a g e s which c o u l d e q u a l l y w e l l a c c o u n t f'or t h e p r e s e n t I F ' - r e s u l t s on &-Fe l i k e t h e p r e - v i o u s o n e , b u t a g z i n b o t h models f a i l t o e x p l a i n t h e MGBbauer r e s u l t s .Conc1.usion.- Peak d o u b l e t s which m a n i r e s t themselves by t h e i r p a r a l l e l a n n e a l i n g b e h a v i o u r h a v e been o b s e r v e d i n i r r a d i a t e d A1 and &-Fe. A t o m i s t i c models i n v o l - v i n g t i l t e d dumbbells and l o c a l i z e d d i f f u s i o n of t h e Fe-ntoms i n i n t e r s t i t i a l c a g e s , r e s p e c t i v e l y , may i n p r i n c i p l e e x p l a i n t h e s e o b s e r v a t i o n s . I n d e t a i l , however, it
i s n o t p o s s i b l e t o p r e s e n t d i s t i n c t models a t t h e ? r e s e n t t i m e . F o r &.-Fe i n p a r - t i c u l a r a model a c c o u n t i n g f o r t h c MBDbauer r e s u l t s s i m u l t a n e o u s l y w i t h t h e p r e - s e n t I F - r e s u l t s i s s t i l l l a c k i n g .
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